# A vector version of the fixed point theorem of cone compression and expansion for a sum of two operators

## Abstract

In this work, we establish a vector version of fixed point theorem of cone compression and expansion for an expansive operator with constant $$h > 1$$ perturbed by a $$k$$-set contraction when $$0 \leq k < h – 1$$. We give the compression-expansion conditions on components to allow the nonlinear term of a system to have different behaviors both in components and in variables. An example is given to illustrate our theoretical result.

## Authors

Lyna Benzenati
Bejaia University, Bejaia, Algeria

Karima Mebarki
Bejaia University, Bejaia, Algeria

Babes-Bolyai University, Cluj-Napoca, Romania

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## Paper coordinates

L. Benzenati, K. Mebarki, R. Precup, A vector version of the fixed point theorem of cone compression and expansion for a sum of two operators, Nonlinear Studies 27 (2020), no. 3, 563-575.